Must the university create an E-Verify case for its interns or unpaid employees?

No, you may only create an E-Verify case for an employee who will receive payment or anything of monetary value, known as remuneration, and has completed Form I-9. Whether or not an intern is a paid employee is based on whether the intern receives payment or remuneration, such as free or reduced housing costs or meals. Check with your legal counsel or human resources professional to determine whether your intern should be considered a paid employee.